2.5x^2=5.75x-2.2

Solution for 2.5x^2=5.75x-2.2 equation:

Simplifying
2.5x2 = 5.75x + -2.2

Reorder the terms:
2.5x2 = -2.2 + 5.75x

Solving
2.5x2 = -2.2 + 5.75x

Solving for variable 'x'.

Reorder the terms:
2.2 + -5.75x + 2.5x2 = -2.2 + 5.75x + 2.2 + -5.75x

Reorder the terms:
2.2 + -5.75x + 2.5x2 = -2.2 + 2.2 + 5.75x + -5.75x

Combine like terms: -2.2 + 2.2 = 0.0
2.2 + -5.75x + 2.5x2 = 0.0 + 5.75x + -5.75x
2.2 + -5.75x + 2.5x2 = 5.75x + -5.75x

Combine like terms: 5.75x + -5.75x = 0.00
2.2 + -5.75x + 2.5x2 = 0.00

Begin completing the square.  Divide all terms by
2.5 the coefficient of the squared term: 

Divide each side by '2.5'.
0.88 + -2.3x + x2 = 0.0

Move the constant term to the right:

Add '-0.88' to each side of the equation.
0.88 + -2.3x + -0.88 + x2 = 0.0 + -0.88

Reorder the terms:
0.88 + -0.88 + -2.3x + x2 = 0.0 + -0.88

Combine like terms: 0.88 + -0.88 = 0.00
0.00 + -2.3x + x2 = 0.0 + -0.88
-2.3x + x2 = 0.0 + -0.88

Combine like terms: 0.0 + -0.88 = -0.88
-2.3x + x2 = -0.88

The x term is -2.3x.  Take half its coefficient (-1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
-2.3x + 1.3225 + x2 = -0.88 + 1.3225

Reorder the terms:
1.3225 + -2.3x + x2 = -0.88 + 1.3225

Combine like terms: -0.88 + 1.3225 = 0.4425
1.3225 + -2.3x + x2 = 0.4425

Factor a perfect square on the left side:
(x + -1.15)(x + -1.15) = 0.4425

Calculate the square root of the right side: 0.665206735

Break this problem into two subproblems by setting 
(x + -1.15) equal to 0.665206735 and -0.665206735.

Subproblem 1
x + -1.15 = 0.665206735

Simplifying
x + -1.15 = 0.665206735

Reorder the terms:
-1.15 + x = 0.665206735

Solving
-1.15 + x = 0.665206735

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.15' to each side of the equation.
-1.15 + 1.15 + x = 0.665206735 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + x = 0.665206735 + 1.15
x = 0.665206735 + 1.15

Combine like terms: 0.665206735 + 1.15 = 1.815206735
x = 1.815206735

Simplifying
x = 1.815206735

Subproblem 2
x + -1.15 = -0.665206735

Simplifying
x + -1.15 = -0.665206735

Reorder the terms:
-1.15 + x = -0.665206735

Solving
-1.15 + x = -0.665206735

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.15' to each side of the equation.
-1.15 + 1.15 + x = -0.665206735 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + x = -0.665206735 + 1.15
x = -0.665206735 + 1.15

Combine like terms: -0.665206735 + 1.15 = 0.484793265
x = 0.484793265

Simplifying
x = 0.484793265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.815206735, 0.484793265}